Prestressed composite structure



Aug. 14, C P CUEN] PRESTRESSED COMPOSITE STRUCTURE Filed Jly 16, 1941 2 Sheets-Sheet 1 y1 1 1 1 1fff1 1 1 -1 @5W/#Mam U10 I 7:3 y l] Y' HTTX C. P. CUENI PRESTRESSED COMPOS ITE STRUCTURE Filed July 16, 1941 2 Sheets-Sheet 2 f lair:

v nwENToR.V CIEM/SNT R41/l af/vl Armen/5y Aug. 14, 1945.

Patented Aug. 14, 1945 PRESTRESSED COMPOSITE STRUCTURE Clement Paul Cueni, Arlington, N. J., asslgnor to Porete Manufacturing Company, North Arlington, N. J., a corporation of New Jersey Application July 1s, 1941, serial No. 402,618l

4 7 Claims.

The present invention relatesto prestressed reinforced concrete and prestress'ed composite structures wherein steel and concrete members or timber and concrete members are combined into one statical unit, designed to carry predetermined loads.

Compositestructures have been known and used for some time, for instance structures like those used in floors for bridges and buildings wherein a series of steel sections, suitably supported by pillars or other permanent members carry a reinforced concrete slab cast on top or around said steel sections, both elements forming one composite beam. To insure the transmission o' the horizontal shear Ibetween the two materials, and thus make an effective statical unit, metallic members, such as cleats, prongs, rods, or elements of various shapes, are attached to Said steel sections and solidly embedded in the concrete slab. If the web of the steel sections is perforated or the upper part of it or the top flange is deformed or stirrups placed around the Asteel section, this may be suillcient to transmit the horizontal shear and no special shear reinforcement may be required.

Composite structures wherein timber is used as the tension member have also been known and used for a. long time, in bridge construction and floors for buildings. The timber joists, suitably supported by pillars or other ypermanent members, carry a reinforced concrete slab cast on top of them and the two elements, suitably connected, form one statical unit, the timber joists taking care of the tensile stresses and the concrete slab taking care of the compressive stresses of the composite section.

Some structures in which shallow steel sections were used, as the tension reinforcement, and which looked like composite sections in the sense this expression is used here, were in fact nothing else than ordinary reinforced concrete structures and always were designed by using the standard reinforced concrete formulas. Such systems, like the Kis system, the Pohlman system and the M system are more or less accurate in design when the depth of the steel section is only a small part of the total depth of the beam. If the depth of the steel sections is a considerable part of the total depth of the structure, the use of reinforced concrete formulas is not correct even if the beams are temporarily supported.

In using reinforced concrete formulas it was assumed that the tension steel is concentrated in one point and that there is no stress variation in the steel. That this is not correct for a4 reinvthe removal of such temporary supports.

forced concrete section with rigid reinforcement at an initial state of load or at the design load is obvious, but, as will be seen later, it is about correct at the ultimate load when the steel section is stressed to the yield point, and if the depth of the steel section is only a small part of the total depth of the beam.

In using composite beam formulas it was assumed that there is a stress variation in the steel, the stress being zero at the neutral axis of the composite section and increasing with the distance, being a maximum at the lowest fibre of the steel section.

Real composite systems like the Alpha System or the Powers System, in the design of which these special formulas for composite sections are used, are applicable to all sections regardless of the ratio of total depth to depth of steel section. In the design of such composite sections it is usually assumed that the composite section carries bothfdead and live load, provided the steel beam has effective intermediate supports during pouring and setting of the concrete. If such supports are omitted it is assumed that the steel section alone carries the dead load and the composite section the live load only. This assumption is correct, because the concrete cannot participate in carrying load until it has set.

It is obvious that with temporary supports less steel is required because the steel section alone does not have to carry the dead load but is helped in that by the concrete. However, such temporary supports add considerably to the expense of the construction, in that it requires considerable labor for the erection, materials to be used therein and a. considerable amount of labor for Often temporary supports are undesirable, too expensive or even impossible. Then the steel sectionv ture, an unsupported beam under certain conditions has the same ultimate load carrying camediate supports during pouring and setting of theA concrete. The disclosure of said application is to be considered as a part hereof.

It is among the objectsof the present invention to provide a new and useful design of composite or reinforced concrete structures involving the use of steel beams or timber joists as tension members, effectively connected to a concrete slab, acting as compression member, in which the design for a specific load is derived by the use of factors not heretofore known in the art.

It is among the objects of the present invention to provide a structure of steel and concrete wherein for a predetermined load the steel area and, therefore, the weight of the required steel is reduced substantially without reducing the adequate factor of safety used for conventional designs.

The present invention is based upon the discovery that the prestresses produced in the steel section by the dead load are gradually eliminated by the live load and do not influence the carrying capacity of the composite section, provided that the pre-stressing is pure bending and does not have any horizontal resultant.' It has been delsubstantial amount without reducing the adequate factor of safety.

'This behavior may be partly explained by that in the breaking state at one point of the beam the entire steel cross-section is 'stressed to the yield point, whereby deformations are produced which are of a higher order of magnitude than the initial deformations caused by the pre-stressing. Pre-stressing, being pure bending, does not produce any resulting horizontal force and therefore cannot influence the resultant tensional force of the composite section at the moment the steel begins to yield. f

This established fact holds true for all cases where the yield point of the steel section is the deciding factor for the carrying capacity of the composite section. It is immaterial lin this case bottom as compressive stresses in the top of thel beam. Then as part of the composite section the entire steel beam is stressed in tension, provided the actual neutral axis of the composite section is above the steel section. The two resultants of the pre-stressing, the tension resultant in the lower part, and the compression resultant in the upper part of the steel section,

b. For composite sections with intermediate temby what causes the bending stress due to prel I stressing is produced (load, dead weight, shrinkage or temperature) as long as the pre-stresses are pure bending and do not produce any horizontal resultant. In the design of any composite section which has an effective shear reinforcement, it is therefore safe to assume that the composite section has to carry the live load only, and to disregard all initial stresses in the steel ,'which may be produced by the dead load due to no temporary supports. I

It is not new to use pre-stressing of steel in reinforced concrete constructions to change the normal course of the stresses produced by load and bring about a new stress distribution quite different from that of normal reinforced concrete and which may favorably affect the ultimate carrying capacity of the structure. But in all such structures heretofore used, exterior forcesy had to be supplied to bring about the prestresses in the steel.

According to the prior methods, by special machines or apparatus a tensional force is applied to the reinforcing bars before the concrete is poured about them. After the concrete has set,

the tensional forceis released and the reinforcing p bars then bring the concrete on the tension side of the structure under compression, thus changing being two parallel forces of the same magnitudev acting in opposite direction, balance each other with respect to the tension resultant of the composite section, which therefore cannot be affected by the pre-stresses in the steel section.

In other words, the dead load of -the structure itself is used to pre-stress the steel beam in such a way that these pre-stresses not only have no effect on the tensional stresses of the composite section but are finally eliminated by them. Thus by forcing the live load, applied on the composite section, to eliminate the dead load stresses in the steel section, the amount of steel required is considerably reduced.

In previous designs of composite sections, 'certain well established formulas have been used. For instance, in computing the tensile stress in steel the following formulas have been used:

a. For composite sections without temporary supports porary supports l. Man-F ML.L.

:Msn

fc c (No. 3)

b. For composite sections with intermediatel temporary supports The Formulas 2 and 4 are also applicable to reinforced concrete sections.

In the above formulas the symbol fa represents the unit tensile stress in the extreme bre of the steel. MD L represents the bending moment due to the dead load. MM represents the bending moment due to the live load. S's represents the section modulus of the steel section alone, and Ss the section modulus of the steel of the composite section. fc represents the unit compressive stress in the extreme fibre of the concrete and Se the section modulus of the concrete in compression of the composite section. The term dead load as used herein includes the weight of the beam plus the first pour of concrete. 'I'he term "live load as used herein includes the second pour of concrete, such as for example in a bridge, a wearing surface, concrete railings, additional road bed, ballast, rails and thelike. The live load also includes the additional dead load such as for example in buildings, floor iill, floor finish, pipes, housings and the like.- In other words, any dead load which is not applied to the steel beam before or at the same time th'e first pour of concrete is made, is included under live load. In addition, the term includes the normal live load, namely the temporary loading of the structure due to traine in a bridge or due to stored goods in a warehouse and the like, or furniture and people in oillce or living rooms.

According to the present invention, a different system of computation is used which is based upon the theory that a composite section may be so designed and constructed that the initial stresses in the steel due to the dead load are gradually eliminated as live load is applied to the composite section.

In computing the tensile stress in the steel, the

following formula is used in accordance with the present invention:

In the accompanying drawings, constituting a part hereof, and in which like reference characters indicate like parts:

Fig. 1 is a cross-sectional view of a. steel section showing the stresses therein due to the dead load alone;

Fig. 2 is a cross-sectional view of a composite beam of steel and concrete showing the stresses in said section due to the dead and live loads at accomplished until shortly before the ultimate load is reached. The value of is is, therefore, more a comparative stress With regard to the factor of safety than` an actual stress. Furthermore, the safe use of the above formula lis subject to the following restrictions:

i. The actual neutral axis of the composite section must be above the steel beam.

2. Definitely no intermediate temporary supports during the pouring and setting of the concrete. If beams cannot be cambered and total deiiection is limited, the dead loaddeflection may be the determining factor for the design of the steel section. Under no conditions can temporary supports be used to reduce deflection.

3. To keep the same factor of safety as for conventional designs in structures built to carry dynamic loads the pre-stresses in the steel plus the stresses due to the live load should not exceed the fatigue strength of the steel for that particular loading condition.

The stresses in the concrete according to the present invention are computed by the use of the formula Se (No. 6)

Comparing this formula with the previously used the moment of failure; A

Fig. 3 is a cross-sectional view of a composite section of steel and concrete, having no concrete around the steel, showing the stresses in steel and concrete due to the dead and live load at the moment of failure;

Fig. 4 is a longitudinal diagrammatic view showing a composite beam suitably supported on permanent supports and subjected to a live load;

Fig. 5 is a cross-sectional view of a reinforced concrete T beam section having a` rigid reinforcement in form of an I beam section andshowing the compressive and tensional stresses in the steel section and the composite section;

Fig. 6 is a cross-sectional view of a composite section in which the neutral axis of the composite section passes through the steel section;

Fig. 7 is a cross-sectional view' of a composite section wherein the concrete encloses the steel section down to the bottom flange, the area of which is increased by attaching a cover Plate by welds or rivets;

Fig. 8 is a cross sectional view of a composite 'section/wherein the tension member is a welded or riveted built up steel section;

Fig. 9 is a cross sectional view of a composite section wherein the tension member is a timbe joist; and

Fig. lo is a longitudinal view of a composite beam suitably supported on permanent supports.

There is provided a beam i (Fig. 1) which, as shown, is of the standard I-beam type. To the right of the beam l is its stress diagram, showing by horizontal arrows the stresses therein due to the dead load. The horizontal arrows 2 represent the compressive stresses therein due to the weight of beam and concrete. 'Ihe maximum compressive stress is at the top of the I-beam.

The arrows 3 show the tension in the lower half of the I-beam due to the dead load, the maximum tensile stress being at the bottom of the I-beam. It will be noted that the magnitude of the compressive and tensile stresses is the same, that their direction is parallel to the longitudinal axis of the beam, .but of opposite sign. Therefore, they do not produce any horizontal resultant.

In Fig. 2 is shown the composite section consisting of the I-beam, the spiral shear reinforcing 4 along the top thereof and welded or othercarried by the concrete slab 8.

Wise secured to the top of beam i. A concrete section 5 surrounds the reinforcing members and is integral with a slab 6, the weight of which is carried by the steel section I. To the right thereof is shown the magnitude and character of the compressive stresses in the composite section. It will be noted that the compression is The arrows 8 show the tensile stressesin the composite section, from which it will be seen that the entire tensile stress is carried by the steel beam l. Long before failure is reached the tensional resistance of the concrete has been overcome and, therefore, Vis entirely neglected as usually in all reinforced concrete designs.'

In Fig. 3 is shown the composite section consisting of the I-beam, the spiral I secured to the top of the beam I, and the concrete slab t, which is supported by the steel section I. To the right thereof are shown the stresses in the composite section, due to the dead and live load at the moment the yield point is reached in the steel section. The arrows show the compressive stresses in the concrete, the arrows I show the tensile stresses in the steel of the composite section. There is no 'concrete in the tension part of the composite section.

In Fig. 2 and Fig. 3 is shown the resultant of the compressive stresses in thev concrete Re, passing through the center of action of. and representing al1 compressive stresses. There also is shown the resultant of the tensional stresses in the steel R passing through the center of action of, and representing all tensional stresses. These two resultants with their rectangular distance 1d determine the resisting moments of the composite section. l

'Ihe resisting moment of the concrete is of no interest in the present investigation. The resisting moment of the steel is represented by the formula:

wherein Mns is the resistingmoment -of the steel (ultimate moment at failure), Ri is the tension resultant, or the tensional force of the composite section.A :id is the rectangular distance between the tension resultant and the compression resultant of the composite section. Rt itself is the area of the tension steel multiplied by the ultimate stress the steel cansustain before failing, namely the yield point. The form-ula for the resisting moment therefore can be written as follows:

As is 'the area. of the steel section, f., is the yield point of the steel. Arxiu-1R.

If none of the three factors of the resisting moment or neither R.t nor jd is changed by the initial stresses in the steel, produced by the dead load, then the dead load has no eifect on the ultimate resisting moment or the carrying capacity of the composite section and, therefore, can be neglected in designing such a section.

Prestressing due to dead load is pure bending -which in any shape of section must produce a compressive force in the upper part of the steel section which is equal to the tensile force at the lower part of the steel section. The two forces are equal in magnitude and parallel but of opposite direction and have no resultant. Therefore, they cannot iniluence the tensional resultant Rt which is parallel to them. For instance: A steel section is assumed with an areaof l square inches and a yield point of 40,000 pounds per square inch. 'I'hen the tensile force Ri available to the composite section is l0 40,000=400,000 pounds. If the pre-stressing in the steel section is at an average of 8000 pounds per square inch, there is a compression resultant in the upper part of the steel section of 5 8000=40,000 pounds and a tension resultant at the lower part of 5X8000=40,000 pounds. This tensional force produced by the dead load uses 40,000 pounds of the available tensile strength and reduces it to 360,000 pounds. But the compression resultant of 40,000 pounds in the upper part of the steel section increases the available tensile strength by 40,000 pounds and restores it to the original 400,000 pounds, because the 40,000

pounds compression cannot. be released without applying 40,000 pounds tensional stresses. It follows that the initial stresses in the steel section cannot iniluence the tension resultant R* of the composite section.

'I'he distance :Id can only be changed by changing the location of the center of action of the tensional stresses of the compositesection. It is obvious that at the moment of failure, when the entire steel section has reached the yield point. the center of action is identical with the center of gravity of the steel section itself, where it is assumed to be in designing the section.

'I'he initial stresses in the steel cannot have any iniluence on the location of the center of action at the moment of failure simply because at that moment they are already eliminated. In the earlier stages of loading of the composite beam the initial stresses in the steel do change the location of the center oi' action of the tensional stresses, but obviously in a downward direction, and so increase the distance 1d and, therefore, the resisting moment. 'I'his is shown in stress diagram Fig. 5d.

Since the magnitude oi the tensional resultant R* and the distance id of the composite section v are not influenced by initial stresses in the steel,

the resisting moment of the composite section, that is the carrying capacity of the composite section, is not iniluenced.

Based upon this, according to the present invention, all initial stresses in the steel beam of v a composite section, in fact any stresses in the steel beam due to dead load, shrinkage, change in temperature, etc. may be disregarded in the design of a composite section, as long as these stresses do not produce any horizontal resultant.

Fig. 4 shows the combination ofthe composite section with its permanent supporting members. Said section 9 is supported at its ends by pillars or the like l0 and Il, respectively. The live load for which the composite beam is calculated is represented by the vertical arrows I2, which cause exlng of the section 9 as shown in broken lines i3. The same principles apply to any length of span. l

In Fig. 5a is shown a reinforced concrete section consisting of steel beam `I, a spiral or other shear reinforcement l, welded to the steel section. a concrete haunch 5 in which steel section I is entirely embedded, and which is poured monolithically with the concrete slab 8. To insure a better bondbetween steel section and concrete, wire mesh or reinforcing bars I4 may be placed around steel section and reach up into the slab. If enough bars are used the shear reinforcement l may be omitted. The steel section has a shallow depth compared with the total depth of the composite section and reinforced concrete formulas may be used for the design. The neutral axis le of the composite section is far above the steel section.

Fig. 5b shows the stress diagram of the steel beam for the stresses due to the dead load. At the lower part is the tension resultant t which equals the compression resultant c at the upper part of the beam.

Fig. 5c shows the stress diagram of the composite section. The line I 6-I l is the zero line representing a state of no stress. A small load applied on the composite section, after the concrete has set, produces stresses as shown by the line l8--I9, which intersects the zero line at the neutral axis I5. The tensional stresses Ain the concrete are neglected as of no importance for ultimate load. A load increase may produce ten- "sional 'stresses in the steel as shown by horizontal g sisting moment of the steel and the resisting moment of the concrete.

Fig. 5d shows the two stress diagrams of Figs. b and 5c combined into one. The concrete stresses are the same as in Fig. 5c. Theoretically, the stress diagram of the steel is as indicated by the line 22-23-24. However, the dotted line 25--23-24 comes nearer the actual con-` dition. It is obvious that the average magnitude of the tensile stresses is the samev as in stress diagram Fig. 5c. The center of action through which R.t passes, however, is farther down than in diagram 5c, which means that the distance id increases and also the resisting moment. The initial stresses in the steel beam due to the dead load, therefore, do not reduce but rather increase the resisting moment of the steel of the composite section.

Fig. 5e shows the stress diagram at the momen of failure. The neutral axis and consequently the compression resultant l'i.c has moved up a little. The tension resultant` l'i.t passes through the center of gravity of the steel section and is, therefore, at exactly the same position as assumed in the design, and as shown in Fig. 5a. The entire steel section is stressed to the yield point and it is obvious that any prestresses in the steel produced by pure bending must balance themselves since pure bending produces the same amount o compressive as well as tensile stresses. i

From the above it follows that in a reinforced concrete sectionl with rigid reinforcement, the initial stresses in the steel section due to the dead load reduce the tensile stresses of the composite section in the upper part of-the steel section by the same amount as they increase the tensile stresses of the composite section in the lower part of the steel section. The tension resultant Rt is therefore not influenced and its center of action but little,4 and if so in a favorable way so that the distance id rather increases than decreases. Since the initial stresses in the steel do not influence either R.t or id,and since Rxid=resist ing moment of the steel of `the reinforced concrete section, it is safe to disregard all initial stresses in the steel in the design of a reinforced concrete section with rigid reinforcement, as long as the initial stresses are pure bending. The dead load cannot produce .any otherv stress in the tension steel of the composite section than the initial stresses produced therein before steel and concrete act together and form a statical unit.

Therefore, such a section is designed to resist only the bending moment produced by the live load, and the bending moment produced by the dead load is entirely neglected.

Fig. 6a shows a steel section I, a shear rein- -forcement 4, attached to thesteel section I and yio Y sion resultant of steel r| and available to balance the isitiite spectively. f

Ycenter of attack. of the` tensile-I in the lower part and t upper part do not produc sultant i with respect r`to'f` ,th of the Ycomposite-se'ctlcinz y section ris in the compressie posite section, it vmeanslth ,y compressive stresses -in the ste'e in me steel with vrespeei. t'ol'the tens vn, of the composite section Rif f 4Iriorder the explanation of how the stresses section are distrlbuted'thestel 'ti l sumed to be a plate with unito unit from top to bottom.u Triest ess then represents also the diag'rsli,f f v pressive and tensile forces of th stee amely f., tension times As andfaco" In a composite sectioninm A" I axis passes through the steel sultant of concrete re.` Th through which R passes isi-"som 11 and rec. 'Ihe line 21 isltheneu section itself.

in the steel. The heavy arrow is of the tensile stresses and ipass'e's 'heavy arrow 3i is the resultant-*ofthe sive stresses passing -throughl'ther 'cntrf :o ofthe compressive stresses. Itcanes.sily,lv

that the two resultants are balanced withre'spect to the tension resultant Rt of `theacomposiy section if the neutralaxis is outside@ th s't tion and the entire steel section composite section, isstressed in 'tension ever, in the section `under considerati n tral axis of the composite .sectionfi through the steel section 'andi -that"par compressive stresses 32 above lids-not' a ilable to balance the tensile stresses. compressive stresses 34, which-"larefibe the neutral axes I5 and I1, are availablet balance the same amount of tensile stressesi32 compressive stresses 32 in thesteelfsection, due to the dead load, increase thereforelthe conpressive stresses in the vsteel `sectionsas pai'tfoflithe composite section, and the tensileastresses'if increase the tensile Lstresses \of.the=@compo'site section. Fig. 6c shows Vthe stress diagrampftheco'mpesite section. Assuming thatthefstressesfincrease with the distance from .thelieutralrfaxis the two triangles formed by the .-zerollneg-Zil and the line 38-39` intersectingat the neutral axis I5, represent recand Rt, respectively. Gombining this diagram with ofirigssb by tracing une vsii- 41, the diagram' f bemand live load stresses, as shown by ,th horizontal arrows 42, 43 and 44, appears.r ,al'iQwsifAZ represent the tensile stressesin'Qth Atecla lso represented by Rt, the. arrowsf43v"`rup slit'vthe compressive stresses in the steel and the arrows 44 the compressive stresses in the concrete. 'I'he two latter form together R, the compression resultant of the composite section. The diagram of the tensile forces reveals that they are increased by the area of triangle 3840'-45 which to bring the neutral `loist 5| by means of has the same area as forces in Fig. 6b. But reduced by the area of triangle cause part of the steel which compression by the dead load is now stressed in tension by a live load applied on the composite section. 'I'hus it is seen that gradually part of the initialstresses in the steel are eliminated. If the actual location of the neutral axis is known the amount of the tensile and compressive forces which are eliminated by the live load can accurately be computed. Using"'the1ocation of the neutral axis given by theusual design formulas to compute'the amount of the eliminated prestresses is always safe, because the actual neutral axis is always farther up than those formulas indicate.

Fig. 6d shows the diagram of ultimate stress. The neutral axis I of the composite section moved up and is about in the extreme libre of the steel section and lower bre of the concrete slab.- Most or all the compressive stresses are taken by the concrete and all the steel, or almost all, is stressed in tension. In this particular case the steel area is in tension and it is obvious that in eliminating the initial compressive stresses in the steel, the same amount of tensile force was made available for Rt. Though the upper part of the steel section does not sustain tensile stresses of high magnitude. the total ultimate tensile force Rt and the distance gid,- are greater than assumed in the design of the section. Therefore, in this particular case one may disthe tensile forces are also 45-I5-46, bewas stressed in regard the dead load even when the neutral axis is in the steel section. 'I'he conditions are not so favorable for all conceivable sections, but it is safe to assume that at least the initial compressive stresses in the steel section which are below the actual neutral axis of the composite section gradually balance an equal amount of initial tensile stresses in the steel section as soon as live load is applied on the composite section. Consequently these two amounts of the initial stresses can be neglected in designing the composite section.

Fig. 7 shows a cross-section beam where the'steel section I is embedded in concrete 41 which may have the form as shown or may fill the entire depth of the structure as indicated by the dotted lines 48. The neutral axis I5 is above the steel section and in the concrete, the beam therefore forms a rectangular section. To increase the area. of the tension steel a cover plate 49 is welded or riveted to the bottom flange 0f steel section I. A shear reinforcement 4 may be attached to the top ange of said of a composite .steel section to insure the transmission of the horizontal shear. t Fig. 8 shows a cross-section of a.- composite beam wherein the tension steel I is an al1 welded section with a smaller top flange and a heavier bottom flange. The concrete slab 5 has a haunch 5 resting on the top flange of the steel section. Such a concrete haunch may be required in order axis I5 of the composite section above the steel section. 50 is a shear reinforcement of 2 bars, bent in wave-like form and welded or riveted to the top ilange.

Fig. 9 shows a composite section wherein a timber joist 5I is used as the tension member. The concrete slab 6 is attached to the timber shear reinforcements 4 in form of spirals, nailed to the joist, or in form of triangular spikes driven into the joists and em- 2,382,139 the triangle of the tensile bedded into the concrete slab. The neutral axis I5 is above the timber section.

Fig. 10 shows the combination of the composite section with its permanent section 9 is supported at its ends bypillars or for most conventional designs and rarely will exceed the allowable deflection. However, due t0 vbut does not affect the ultimate load of the composite section.

To show the saving obtained by the use of the present invention, one may compare the design with that obtained by using the prior formulas. In so doing, according to the present formula, one assumes that the dead load stresses in the 1. A beam with temporary intermediate supports where it is assumed that the composite section carries both dead and live load, and

2. A beam without temporary supports where it is assumed that the steel alone carries the V dead load and the composite section the live load only.

Example 1 MILL. 1,960,000 inch pounds MLJ.. 2,340,000 inch pounds tobe 12.

su 4770 in.3 s; 17s in.=

the extreme nbre stresses in steel and concrete Concrete, due to L.L. `fswLM)I491l lbs./sq. in.

2,340,000' 17g- 13,150 lbs.lsq. in.

'Ihe design according to the prior formulas, for

Steel, due to L.L. f.=

case No. 1 where temporary intermediate supm The extreme nbre stresses in concrete and steel are:

prooied by 2" of concrete. The bending moments are:

Mba.. 241,800 inch pounds Mm.. 590,200 inch pounds The allowable extreme nbre stresses are: steel 18,000 pounds per square inch, concrete 800 pounds per square inch; n is assumed to be 15.

A design made in accordance with the present invention shows that a 12 inch light beam section with a weight of 16.5 pounds per linealioot is required. The section moduli o! steel and concrete o( the composite section are:

se 1700 in.l s. 37.501;a

u The extreme nbre stress in steel and concrete are:

Concrete, due to L.L. f=

Concrete, due to D.L.+L.L. f= v 320 pounds per sq. in.

1,960,00044,340,000= 772 1bs per Q in. Even if it is computed on the total load, the stress 5570 in the concrete is only Steel, due to D.L.+L.L. f.= 811 000 f=--" =456 pounds per sq. in. 1,900,000+2,340,000 25 1780 18,000 lbs. per sq. 1n. I 239 Steel, due to L.L. f,=

In a design according to the priorformulas for 57goo=15g00vpounds per sqjn,

case No. 2 where notemporary supports are used, there is required a 16 inch wide nange section, having a weight of 114 pounds per lineal foot; The section moduli for the steel section and the composite section are:

'I'he extreme nbre stresses in steel and concretel 35 Concrete, due to L.L. f= Y Due to L.L. f.== 305 7,680 lbs. per sq. in.

- Total stress f,=17,880 lbs. per sq. 50 The difference between the dead loadmoment of case No. 1 and case No. 2 is due to the dinerence in weight of the steel section.

The saving in steel by the present invention'as compared with the prior art is as'follows: 55

Compared with caseNo. l:

16 WF88, total weight 40x88 3250 lbs. 16 WF 64, total weight 40X64 :72560 lbs.

In addition to 960 ibs. more sei, me No. 1 requires-intermediate supports. i y

Compared with case No. 2: 65 16 W'F 114, LOSJ.b Weight 411x114 4560 1bn.

16 WF 64, total Weight 40X 6.4 '2560 lbs.v l

Saving per. beam 2000 lbs.

Example z lconcreti: slab is 4" thick 3nd the structure fire- =10,200 lbs. per sq. in. 5

f|=r24110500= 13,7810 pounds per sq. in.

17.5 section modulus of steel section alone. This stress is not taken into consideration according to the present invention.

The design according to the prior formulas, for case No. 1, where temporary intermediate supports are used, requires a l2 inch lightv beam section with a weight of 22 lbs. per lineal foot. The

section moduli of steel and concrete of the`com posite section are:

s.=1s90 in.3 s.=4 0.2 ins l extreme'nbre in concrete andsteel concrete: 'due wgnL. +11.. f.;

Steel: due to D.L.+L.L. f.=.

ms-w =17600 lbs. sq. in. In a. design according to the prior formuiasror case No. 2- where no temporary supports are used, a 12 inch wide flange section (Standard Mill 430 lbs. per sq. in.

' Beam) with aweight of 28 lbs. per square inch is required. 'Ihesectionmoduli of steel and concreteiu'c:

.ca -.19051101 s.1=s2.s me fs.=57.4 in# The stresses in steel and concrete are:

Concrete:

adagio L.L.f.=57%=2s01bs. peg-,sq in.

Steel: l

due to-D.L. 1.--3-2-:6-#582'80 lbs. per sq. in.

l Tois1f 18,2001b's. per sq. in.

The saving in steel by the present invention as compared with' the prior art is as follows:

Compared with case No. l:

12 L.B. 22 total weight=20 22 =440 lbs. 12 L.B. 16.5 total Weight=20 16.5=330 lbs.

Saving per beam= 110 lbs.

` Compared with' case No. 2:

' 12 M.B. 28 total Weight=20 28 =56O lbs. 12 M B. 16.5 total weight=20 16.5=330 lbs.

Saving per beam=230 lbs.

In Example l the saving in fthe weight of steel in favor of the new design amounts to 21 compared with case No. 1 design, and to 44% comparedwith case No. 2 design. In Example 2 it is 25% compared with case No. 1 and 41% compared with case No. 2. Assuming a cost of ve cents per I'he present invention makes it possible to build a structure in composite design with less steel than is required for reinforced concrete design.

Such a composite section is ea'sier to erect, does not require temporary supports, is lighter and saves in concrete. This saving in concrete is considerable vwhere no ilreproofing is required, less pronounced where the steel has to be protected. Besides, such-a composite section h'as technical advantages against a reinforced concrete section. shrinkage of the concrete, which produces compressive stresses in the top flange of |the steel section of a higher magnitude than the tensile stresses produced in the bottom iiange produces, therefore, a horizontal compression resultant in the steel section which tends to reduce the tensile stresses of the composite section produced by the live load. shrinkage may increase the tensile stresses in a reinforced concrete structure. Cracks in the concrete on the tension side which may be harmful in reinforced concrete are of no importance in composite design because no structural concrete is required there. Plastic ow of concrete in such a composite section in less pronounced, because the concrete receives less permanent stress, and its influence is therefore much less than for a reinforced concrete beam.

The heretofore known systems of pre-stressing help the concrete by increasing its area of compression and by making impossible tensional stresses in the concrete on the tension side of the structure. Therefore, with the same concrete area greater stresses can be sustained and 'the disadvantage of concrete cracks on the tension side is eliminated. However, considerably more steel area is required or steel 'with much higher tensile strength.

The system according to the present invention helps the concrete somewhat, as the concrete does not receive dead load stresses, and it makes possible a considerable reduction in steel area. Conpound of steel, the actual saving in cost per beam initial dead load stresses being entirely neglected,

crete cracks on the tension side of a composite section are of no importance, as the concrete there has no structural function. Whereas th'e prestressing in the heretofore used pre-stressed reinforced concrete structures il costly and complicated and takes much time, the prestressing according to the present invention does not require any expense or work, neither in the designing nor in the erecting of the structure. Besides all temporary supports are eliminated which also means a saving in cost.

Heretofore, composite concrete and timber floors were not usedextensively because the concrete slab is more costly than door boards and the higher weight of the concrete increases the dead load so much that the saving by the composite action is almost balanced. With a composite iloor construction of concrete and timber according to the present invention, the entire dead load is disregarded and the saving, therefore, considerable. Y

In the above description the invention has been applied to simple beams wherein only positive moments occur. The invention is not limited thereto but applies as well to continuous beams wherein positive and negative moments occur. In the negative moment the stresses are reversed and the steel section, due to the dead load, is stressed in tension in the top flange, and incompression in the bottom flange. The live load applied on the composite section produces compressive stresses in the steel section, as against tensile stresses in the positive moment.

In the above description the invention has been applied to pre-stresses due to the dead load of the structure itself. It is obvious that some load could be applied to the steel section during pouring and setting of the concrete and then, when the concrete has set, the load is removed. That load produces additional initial stresses in the steel, similar to the initial stresses produced by the dead load. These initial stresses will have no influence on the ultimate load of the composite section. Then, when the load is removed, the deection of the composite section will diminish and the composite section now sustains the release moment. This means that the steel section sustains compressive stresses and the concrete tensile stresses. This stress, with the opposite sign as the stresses produced by the live load, could be used to balance part of the live load stresses. However, it is doubtful that the small additional saving will offset the additional cost for applyin and removing the load.

What I claim is:

1. A method of making a prestressed composite structure which comprises providing substantiallyv 2. A method of making a prestressed composite structure which comprises providing substantially.

rigid reinforcements in the form of structurall shapes having shear reinforcing, mounting the same on permanent supports without intermediate temporary supports, pouring concrete about said reinforcements to impart dead load prestresses of pure bending thereto allowing the concrete to set, the stresses in said structure such that the live load applied on the completed reinforced concrete beam acts to neutralize said `livrestresses, the area of said reinforcements being sufficient to take the live load stresses only, the initial dead load stresses being entirely neglected, the stresses in the reinforcements being computed according to the formula wherein fs represents the unit tensile stress in the extreme fiber of the reinforcing material, Mm.. the bending moment due to the live load, and Ss the section modulus of the composite section, the positioning of the concrete relative to said structural shapes being such that the neutral axis of the composite structure is above said structural shapes.

3. A method of making a prestressed composite structure which comprises providing substantially rigid reinforcements in the form of structural shapes having shear reinforcing, mounting the same on permanent supports without intermediate temporary supports, pouring concrete about said reinforcements to impart dead load prestresses of pure bending thereto allowing the concrete to set, the stresses in said structure such that the live loadapplied on the completed reinforced concrete beam acts to neutralize at least most of said prestresses, the depth of said structural shape being a substantial portion of the depth of said composite structure, and the neutral axis of the composite section being above said structural shape.

4. A method of making a prestressed composite structure which comprises providing substantially rigid reinforcements in the form of structural shapes having shear reinforcing, mounting the same on permanent supports without intermediate temporary supports, pouring concrete about said reinforcements to impart dead load prestresses of pure 4bending thereto allowing the concrete to set, the stresses in said structure such that 'the live load applied on the completed reinforced concrete beam acts to neutralize said prestresses, the area of said reinforcements being sutlicient to take the live load stresses only, the initial dead load stresses being entirely neglected, the sum of said prestresses and the stresses due to the live load being less than the fatigue strength of the reinforcing material for the calculated live load, the positioning of the concrete relative to said structural shapes being such that the neutral axis of the composite structure is above said structural shapes.

5. A method of making a prestressed composite structure which comprises providing substantially rigid Areinforcements in the form of structural shapes having shearreinforcing, mounting the same on pennanent supports without intermediate temporary supports, pouring concrete about said reinforcements tof impart dead load prestresses of pure bending thereto allowing the concrete to set, the stresses in said structure such that the live load applied on th completed reinforced concrete beam acts to neutralize said prestresses, the 'area of said reinforcements being suflicient to take the live load stresses only, the initial dead load stresses being entirely neglected, the resisting moment of the reinforcements being represented by the formula wherein Mal represents the resisting moment of the steel, R the tensionI resultant, and id the rectangular distance between the tension resultant and the compression resultant of the com;- posite section, the positioning of the concrete relative to said structural shapes being such that the neutral axis of the composite structure is above said structural shapes.

6. A method of making a prestressed composite structure which comprises providing substantially rigid reinforcements in the form of structural shapes having shear reinforcing united therewith, mounting the same on permanent supports without intermediate temporary supports, cambering said beam to reduce the deflection due to the dead load, pouring concrete about said reinforcements to impart dead load prestresses'of pure bending thereto, allowing the concrete to set, the stresses in said structure such that the live load applied on the completed reinforced concrete beam acts to neutralize said prestresses, the area of said reinforcements being suilicient to take the live load stresses only, the initial dead load stresses being entirely neglected, the positioning of the concrete relative t0 said structural shapes being such that the neutral axis of the composite structure` is above said structural shapes.

7. A method of making a prestressed composite structure which comprises providing substantially rigid reinforcements in the form of structural shapes having shear reinforcing united therewith, mounting the same on permanent supports without -intermediate temporary supports, pouring concrete about said reinforcements to impart dead load prestresses of pure bending thereto, allowing the concrete to set, the stresses in said structure being such that the live load applied on the completed reinforced concrete beam acts to neutralize said prestresses, the area of said reinforcements being suiilcient to take the live load stresses only, the initial dead load stresses being entirely neglected. the positioning of the concrete relative to said structural shapes being such that the neutral axis of the composite structure is above said structural shapes, the prestresses in the steel plus the stresses due to the live load not exceeding the fatigue strength of said steel for a predetermined loading condition; y CLEMENT PAUL CUENI. 

